It wasn’t until I rushed out of my interview with Nancy Meyers, five panicky minutes early, in order to express some milk in Claridge’s hotel bathroom, having given birth three weeks ago that I realised something: I wasn’t interviewing Meyers – I was a character in one of her movies.

Throughout her 35-year career, Meyers – who is, by some measure, the most commercially successful female writer and director in Hollywood – has focused on what she describes as “telling women’s stories”.

These stories have included young widowhood (Private Benjamin), working mothers (Baby Boom), fiftysomething love affairs (Something’s Gotta Give), and divorce (It’s Complicated). All blend tough themes with comedic scripts, dramatic issues with light-hearted one-liners. Her hugely lucrative comedies, such as Father of the Bride and What Women Want, also maintain a deceptively easy-going focus on beady-eyed human stories.

This has earned Meyers millions of fans, some of whom create Pinterest pages about her films and throw Meyers-themed parties. It has also attracted the derision of (male, usually, but not always) critics and, more upsetting for Meyers, the occasional feminist writer. “I remember being misunderstood by critics 30 years ago,” she shrugs, yet recalling criticism of one of her films in Susan Faludi’s seminal 1990 feminist book Backlash causes Meyers, a proudly self-described feminist, palpable pain. (Faludi cited Baby Boom as proof that Meyers had “internalised” Hollywood’s anti-women messages; for whatever it’s worth, I disagree with Faludi about that.)

Nonetheless, Meyers’ continued interest in the personal and largely female screenplay – especially at a time when Hollywood has never been more interested in what she calls “the Superman, Batman, Anythingman” films – has made her more of an anomaly in the business than ever. After all, she is a 65-year-old woman and a bona-fide A-list Hollywood director whose movies make hundreds of millions of dollars. She was, she says, “unusual” in 1979 when she started out, aged 29, with Private Benjamin. But that she is still seen as an aberration in 2015 surprises no one more than her.

In her latest film, The Intern, Robert De Niro plays Ben, an unlikely work-experience placement at a New York fashion website run by Anne Hathaway’s character, Jules – a hard-working woman, who is married and has a small daughter. Given her interest in the subject of working mothers, some might think it unsurprising that Meyers asks me twice about my experiences so far in motherhood and even remembers the names of my babies an hour later to tell her sister, who joins us in the hotel room at the end of the interview. But the truth is, most Hollywood interviewees barely bother to note a journalist’s name, let alone those of their offspring.

Talking with Meyers and her sister is a lot like slipping into a Meyers film: there is female bonding and gentle laughs. But there is also just enough sharpness beneath the surface to spike any suggestions of saccharine (when I make some clumsy comment about my mother “dragging” my father to see It’s Complicated, Meyers interrupts with riled briskness: “Why did he have to be dragged?”) Meyers admits that she has often used herself as the inspiration for her movies: when she and her then partner Charles Shyer made Baby Boom, they were expecting their second daughter (“I pretty much went into labour in the editing room”). Meanwhile, Something’s Gotta Give and It’s Complicated both feature fiftysomething divorcees, something Meyers understands well, having divorced Shyer in 1999, after 19 years of marriage. In this regard, The Intern represents something of a change for the director, given that it lacks an obviously Meyers-esque character.

“That’s right – there’s no Meryl Streep or Diane Keaton. I can’t keep making that movie, and I felt I’d done it pretty well a couple of times,” she says. But she adds that, as “a working grandmother”, she wanted to “put that character of the working mother out there again, and to show that her daughter is not suffering because her mother works”.

Anne Hathaway & Robert De Niro in The Intern. Photograph: Francois Duhamel/Allstar/Warner Bros

I’m a big Meyers fan, but The Intern is not my favourite of her films. I never really believed in De Niro’s character, a 70-year-old gentleman whose only desire is to help out clueless millennials. Still, it is a pleasure to see a movie in which a woman is not punished for being professionally ambitious. This might seem a pretty low bar, but given the cinematic trope of female characters quitting their jobs to prove their love for a man (The Devil Wears Prada, Trainwreck), The Intern looks almost revolutionary by comparison.

“There aren’t enough movies that show working women who are content at their job, good at their job and good bosses. If I see one more movie where a woman is a horrible boss who is hated by her employees …” Meyers says with an eye-roll.

Nonetheless, some critics have complained that the film suggests that, as Guy Lodge wrote in Variety, “behind at least one successful woman stands an older, wiser man”.

Meyers bristles at the criticism: “It’s just a ridiculous thing to say. I’m very happy to go on the record saying that human beings need other human beings and that’s what I’m saying. Someone’s watching Jules’ back – that he’s a man is not the point.”

More telling, Meyers says, is the number of male journalists who have described Hathaway’s character as “a workaholic”, simply because she takes her job seriously. “Men don’t even realise they’re saying this kind of stuff,” she says. Then there is the eternal obsession with interiors in her films. Jibes about the gorgeous houses in Meyers’ movies have become something of a schtick among film writers and bloggers. Recently Jezebel.com ran a quiz, “Which Nancy Meyers kitchen are you?”, while Vogue.com invited readers to “Shop Nancy Meyers’s Most Enviable Interiors”. It’s true, the houses in her films are lovely, but no more so than those in, say, Judd Apatow’s movies, which are never mentioned in reviews. Meyers is exasperated by this, but loath to complain and draw more attention to the subject. Still, I suspect that she feels, as I do, that this focus on the surface of her movies, reducing them to catalogues, is a way of belittling her, her audience and the female stories she tells.

Yet all this is small potatoes compared with the bigger problem Meyers contends with: sexism in the film industry. The statistics are depressingly well-known: of the 100 highest-grossing films in 2014 only 1.9% were directed by women and only 12% featured female protagonists. For Meyers, who has been working in this world for nearly her entire adult life, this is familiar stuff. When she started out on Private Benjamin, the studio wrote into her contract that she must never be alone on set without her male co-producers.

“Of course, me in 2015 would have taken a red pen to it and said, ‘That’s ridiculous.’ But 29-year-old me, making my first movie, didn’t go to the mat about it, so it remained in the contract. I don’t know what they were thinking,” she says.

Perhaps they imagined you’d spontaneously burst into pregnancy without supervision, I say.

“I was pregnant, but I hid it! Can you imagine? So, yes, things have moved on from then. But do women have equal rights in Hollywood? No.”

What I don’t understand, I say, is that given that her films are so successful, and made for relatively little, why don’t studios look at them and say: “We should make more movies like these?” or, “Maybe we should trust more female directors”?

Meyers’ career began in 1979 with Private Benjamin, starring Goldie Hawn. Photograph: The Kobal Collection

She nods in agreement while making an exasperated sigh: “My kind of movie is not the kind of film that studios have wanted to make for a while now. Instead, it’s been all comic-book movies, gigantic action movies and guy comedies. As for why aren’t there more women [directors], there has been somewhat of a guilt-free environment and [studios] have been making a certain kind of film for a while, and, for whatever reason, they think a man would be better at directing dinosaurs, or flying people, or whatever. But I know there are plenty of super-game women who would want to make those films.”

When I’ve asked studio executives about the lack of female directors, they always give the same two contradictory answers: that women don’t feel comfortable being in charge, or that people don’t like taking orders from bossy women.

Meyers looks more frustrated than ever: “OK, well the first part we know is not true – women are in charge of so much, and enjoy being in charge. And people don’t like bossy women? You know, I have directed very big actors and what they like is leadership. So [that feeling] doesn’t exist in the acting community. But does it exist in the executive community? It’s obvious, it’s a boys club. But I honestly believe things are changing. I’ve been doing press on movies for 35 years, and this is the first time anyone’s talked to me about this, and everyone I’ve talked to has asked me about this. I think the conversation is out there now.”

But, in terms of depictions of women in movies, are things worse than when she started?

“Well, I don’t see a lot of movies telling stories about complicated women with real problems,” she says, “and studies tell you that’s true. So I can’t say it’s gotten better. I have to be honest with you, I think it’s gotten worse.” But in classic Meyers fashion, she delivers the bad news with a warm laugh.

•Nancy Meyers was one of the speakers at the BAFTA & BFI Screenwriters’ Lecture Series (you can read her lecture here). The Intern is released on Friday 2 October.